For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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Calculating probability that 5 dice rolls will produce an average of 3.5

We are carrying out a dice game which involves 5 people rolling dice and passing buttons equal to the number rolled . We have to work out the probability that we will get an average of 3 .5 items ...
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2answers
48 views

Dice probability, Heaven or Hell [on hold]

You're at the gate of Heaven and St. Peter asks you to play Dice with him. If you roll a 5 or 6, he'll let you into Heaven. However, if you roll a 2,3 or 4, you'll be sent to hell. If you roll a 1, he ...
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2answers
33 views

Find dependent event when two dice are thrown simultaneously.

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die $B$ shows up two and $E_3$ is the event that the sum of ...
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0answers
40 views

Roll dice and get score except when you get 6 where you lose everything [on hold]

At what score to stop when you roll a dice under these conditions: -if you get 6 you lose all your score -You score is the add up of all rolls
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0answers
26 views

Can someone help me balance this game (probability question) [on hold]

A team of 9 vs a team of 1. Each round each of "the 9" roll a die to "attack" and "the 1" rolls 9 dice to "defend", the nine dice are preassigned to attackers before the roll, "the 1" cannot choose ...
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1answer
29 views

Given three six-sided dice, what is the probability that the value of the third will be greater than the sum of those of the first two?

A die is rolled three times, or three dice are rolled. What is the probability that the third die values greater than the sum of the first two? (assuming six-sided dice, but I would be interested in ...
0
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1answer
28 views

Creating $Y \sim U[1, \dots, 6] + U[1, \dots, 6]$ as a function of $X_1, X_2, X_3 \sim U[1, \dots, 6]$

The Three Indistinguishable Dice Puzzle from standupmaths The problem therein can be summarized as follows: You have three dice rolls. Each die is indistinguishable from the others. However, using ...
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3answers
530 views

You cast a pair of dice. If you get a 6 and an 8 before 7 comes up twice, you win. What is the probability of winning?

You cast a pair of dice. If you get a 6 and an 8 before 7 comes up twice, you win. What is the probability of winning? What I tried was \begin{align*} P(X=6) & = \frac{5}{36}\\ P(X=8) & = ...
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4answers
1k views

Rolling a die until two rolls sum to seven

Here's the question: You have a standard six-sided die and you roll it repeatedly, writing down the numbers that come up, and you win when two of your rolled numbers add up to $7$. (You will ...
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2answers
36 views

What is the probability of these questions?

What is the probability of throwing $2$ dice, and the first one is a $6$? (Given that one of them is a 6.) My solution says that it's $\frac{6}{11}$, but I have no clue why. The other one is: What ...
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1answer
640 views

How to use N indistinguishable dice to simulate 1 roll of N-1 dice? [closed]

If I use 3 indistinguishable dice to simulate 1 roll of 1 die. I can use this formula "(SUM % 6) + 1". There SUM is the total amount of the three indistinguishable dice added together, 6 is the max ...
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3answers
1k views

Probability of three dice falling in the same quadrant of a box

This is surely really basic for most people here but it's tripping me up. You get a box and draw lines to split it up into 4 parts. I got asked what the probability was that when rolling three ...
2
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0answers
41 views

Roll two fair dice, what is the expected value of rolls such that the sum of the two faces is the multiple of 6.

I was thinking that there were 2 cases: (1) $\\$ $X_{1}+X_{2}=6$, and the probability would be $\dfrac{5}{36}$. (2) $\\$ $X_{1}=X_{2}=6$, and the probability would be $\dfrac{1}{36}$. I am now ...
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1answer
48 views

Probability of being able to make a given number with two out of xd6

I'm an amateur games designer, and am working on a mechanic which involves rolling on a table with numbers running from 2-12 - the full range of possibilities from adding together two six-sided dice. ...
0
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2answers
35 views

Rolling dice against each other?

After doing some research, I found that the probability of rolling an n-sided die against another, equivalent die and landing a higher number on the first rolled dice to be ((n−1)/2)/n, where n is the ...
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2answers
28 views

Probability of Rolling a $1$ on an $n$-Die in $r$ Attempts

I roll an $n$ sided die, numbered $1 \to n$. If I roll a $1$, I walk away; otherwise, I roll the die again. This process could repeat indefinitely. What is the probability, $P(n,r)$, that I will roll ...
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0answers
26 views

7th Sea 2e: Grouping dice results into sets of 10 vs doing the same with Tarot cards.

Note: While an interesting problem on its own, it also struck me as an excellent example of how marvelous the human brain is, as it is able to almost effortlessly negotiate a task that (at least to ...
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4answers
1k views

Probability of obtaining a heads on the coin before a 1 or 2 on the die?

I came across this question recently and can't seem to find the correct approach. Any help would be appreciated! An experiment consists of first tossing an unbiased coin and then rolling a fair ...
5
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1answer
51 views

Probability of rolling dice twice

Did I calculate the correct probability for these simple scenarios: 1: What is the probability of rolling 3 and 4 with two dice in two rolls? If you roll either 3 or 4 in the first roll, you put ...
0
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1answer
49 views

If you roll four dice what is the probability of getting at least two sixes?

First of all, I know there are a lot of these and similar questions already online but I am trying to solve this on my own and I need you to tell me what I am doing wrong. So, in class we solved ...
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1answer
22 views

Probability of $3$ doubles when two dice roled $4$ times

I thought that when rolling two dices to get only pairs is for a single roll $\frac{1}{6}$ for two $\left(\frac{1}{6}\right)^2$, and for three $\left(\frac{1}{6}\right)^3$. But since I have 4 rolls ...
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0answers
62 views

How to statistically beat this dice game?

There is a dice game on this site where you can bet a video game's currency in games. I was wondering if any of the more statistically minded could come up with a way of beating the system? The game's ...
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1answer
79 views

Dice probability with limited reroll

What is the probability of getting 2 successes when 3 dice are rolled once, and then one die is optionally rerolled? $$ n = \text{Number of dice} = 3 $$ $$ p_s = \text{Single die success probability ...
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1answer
57 views

Rolling a biased dice, Multinomial probability

What is the easiest way to answer this question. Lets say you had a biased 6-sided die P(rolling '1') = P(rolling '3') = 0.1 P(rolling '2') = P(rolling '4') = P(rolling '6') = 0.25 P(rolling '5') ...
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2answers
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2
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1answer
37 views

How many rolls of two dice are needed so that the probability of rolling a double six within this number of rolls is at least $50\%$?

My approach: How many rolls of two dice are needed so that the probability of rolling a double six within this number of rolls is at least $50\%$? Let $X$ be the number of required rolls. ...
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2answers
31 views

Rolling the results at the same time as the check

I was in a roll playing game last night. In combat we throw 3 six sided dice when we attack and roll some amount of dice if we hit our target by rolling high enough on the attack (for example the dice ...
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0answers
36 views

Most Probable Sum for Dice Rolls

Hey so I discovered this formula for finding out the most probabble result when rolling a certain number of f-sided dice. Could you check it and tell me why it is so? ...
0
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1answer
21 views

Probabilities of reoccuring draws in a stack of cards

Let's say I have a stack of $12$ cards where only one card in the set is a golden card. The cards are displayed face down on the table in a $3\times4$ pattern and I can choose one card at the time. As ...
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2answers
235 views

Rolling $n$ $k$-sided dice and discarding the lowest $m$ of them.

In this question I will use the notation $\Bbb{E}(n,k,m)$ to refer to the expected average of rolling $n$ $k$-sided dice and discarding the lowest $m$ of them. The most trivial response happens ...
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2answers
44 views

Rolling four dice and the difference between predictions

Four standard dice are rolled. What are the chances of: 1.) Rolling three sixes and one five? 2.) Two sixes and two fives? 3.) Exactly one six? 4.) Four different numbers? Here is my thought ...
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4answers
878 views

On the probability of getting the same number for three dice

I found the probability of having the same number when throwing 3 dice to be $1\times\left(\frac16\right)^2$. In addition, I don't understand how do people get the equation ...
2
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1answer
40 views

Comparative Dice Statistics

I am part of a role playing game where we roll dice to set our statistics. Our current system is to roll 4d6, reroll the lowest of the 4, then keep the highest 3 out of the original 3 and the new one ...
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1answer
27 views

Odds of Winning a Scratch Card

I have a scratch card that has 36 spaces that can be scratch. 9 of the spaces have a winning symbol and 27 spaces have an "X". I am allowed to scratch as many spaces until I either get the 9 winning ...
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0answers
46 views

Alternate Answer for a probability fair dice game using conditional probability

The problem: In this game, if two dices give: \begin{cases} 7 \text{ or } 3, \text{ then the player wins} \\ 2,\space 11 \text{ or } 12, \text{ then the player loses} \\ \text{else, then the game ...
4
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2answers
53 views

Probability of winning dice roll-off with a re-roll

I am looking to find the probability of winning a basic dice roll-off using a 6 sided die if one of the players can re-roll their die. The main thing that is throwing me off is that player 2 can ...
2
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2answers
94 views

Probability of rolling a sum of at least 18 with 10 6-sided dice

I'm trying to work out how to do this, and I'm very stuck. My grasp of probability is shaky to begin with, and generally with probability questions, I list out cases. Due to the number of ...
0
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1answer
51 views

Probabilities for rolling multiple dice and getting one number or greater

I am interesting in producing a table of probabilities for dice rolls. These are standard 6 sided dice. What is the probability that for rolling X dice, Y dice will roll (hit) at least number Z or ...
2
votes
1answer
56 views

probability of not getting same number twice in a row after n die rolls

Having rolled a die $n$ times, I want to determine the probability of not getting any number twice in a row. If I wanted the probability of not getting any number three times in a row, I could use the ...
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1answer
62 views

Probability of rolling higher than $N$ by summing the highest $X$ number of dice out of a set $Y$ number of dice, each with $Z$ sides.

I'd like help finding a formula for the probability of rolling higher than a target number, $N$, by summing the highest $X$ number of dice out of a set $Y$ number of dice, each with $Z$ sides, ...
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2answers
45 views

Expected payment of a roll of dice with rerolls

We've got the following game: You roll two dices. You get paid equal to the number rolled. Additionally, if you roll doubles, you reroll (Same rules apply to that roll. That means there's not limit ...
1
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1answer
37 views

Three fair dice are rolled one time. What is the probability of at least one $6$?

I think the answer is $10/216$, but I am not sure. I did it by brute force though, and would like to know the background, as well as knowing if $10/216$ is correct. Edit: now i think via brute force, ...
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3answers
82 views

Distribution of the sum of $N$ loaded dice rolls

I would like to calculate the probability distribution of the sum of all the faces of $N$ dice rolls. The face probabilities ${p_i}$ are know, but are not $1 \over 6$. I have found answers for the ...
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3answers
304 views

Exploding (a.k.a open-ended) dice pool

Say we role $n$ identical, fair dice, each with $d$ sides (every side comes up with the same probability $\frac{1}{d}$). On each die, the sides are numbered from $1$ to $d$ with no repeating number, ...
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1answer
30 views

Covariance of dice tosses that result in 1 or 2 (fake proof)

Question: Consider n independent tosses of a $k$-sided fair dice. Let $X_i$ be the number of tosses that result in $i$. What is the covariance $\mathrm{cov}(X_1,X_2)$ of $X_1$ and $X_2$. ...
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2answers
104 views

Suppose you roll two dice. Find the probability that you roll an 8, provided you roll a 7 or 8 first?

In the gambling game "craps," a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up sides of the six-sided dice. The bettor wins on the first roll if the sum is ...
2
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1answer
62 views

Expected number of dice rolls of an unfair dice to roll every side equally many sides

I am having trouble with solving the following problem: The probability that a $d$-sided dice lands on its $k$th side is equal to $p_k$ for $k\in \{k\in\mathbb{N},k≤d\}$ and $p_1+p_2+p_3+...+p_d=1$. ...
0
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0answers
36 views

Number of ways a dice can roll every side equally many times for the first time after x rolls

This problem is best viewed as a walk on a $d$-dimensional integer lattice with integer steps corresponding to various results of a dice roll. For a normal 6-sided dice, these would be ...
3
votes
1answer
40 views

Can you create non transitive dice for any finite graph?

Let's say you have a finite directed graph, with no two nodes that point at each other. Can we assign each node a dice, so that each node beats the node it is pointing at. This is easy for acyclic ...
3
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3answers
40 views

Probability of Rolling a Pairwise Seven rolling $4$ Dice

My friend posed this problem to me. He wrote a computer program to generate all possible combinations of dice and counted the cases with pairwise $7$'s. I thought that the problem had a simpler ...